The next number is 12.
The rule is
Un = (2n4 - 27n3 + 123n2 - 214n + 120)/2 for n = 1, 2, 3, ...
The sequence 0, 3, 8, 15 can be understood by observing that each term can be expressed as (n^2 - 1), where (n) is the position in the sequence starting from 1. For example, (1^2 - 1 = 0), (2^2 - 1 = 3), (3^2 - 1 = 8), and (4^2 - 1 = 15). Following this pattern, the next term for (n = 5) would be (5^2 - 1 = 24). Thus, the next number in the sequence is 24.
10, 8, 6, 4, 2, 0, -2, -4
16
64
The sequence alternates between multiplying by 2 and then adding 2. Starting with 2, it goes to 4 (2×2), then to 8 (4×2), followed by 10 (8+2), and then to 20 (10×2). Following this pattern, the next operation would be adding 2 to 20, resulting in 22. Thus, the next number in the sequence is 22.
The sequence 0, 3, 8, 15 can be understood by observing that each term can be expressed as (n^2 - 1), where (n) is the position in the sequence starting from 1. For example, (1^2 - 1 = 0), (2^2 - 1 = 3), (3^2 - 1 = 8), and (4^2 - 1 = 15). Following this pattern, the next term for (n = 5) would be (5^2 - 1 = 24). Thus, the next number in the sequence is 24.
13, 21 - it is the Fibonacci sequence
10, 8, 6, 4, 2, 0, -2, -4
The solution is 8. Here's the explanation: Differences between numbers that form sequence 200, 188, 152, 80, 8, ? form another sequence 12,36,72,72,? the solution of which is 0 because they are multiplied with 3, 2, 1, 0 respectively (72x0=0). When you apply 0 to the original sequence you get 8-0=8.
The solution is 8. Here's the explanation: Differences between numbers that form sequence 200, 188, 152, 80, 8, ? form another sequence 12,36,72,72,? the solution of which is 0 because they are multiplied with 3, 2, 1, 0 respectively (72x0=0). When you apply 0 to the original sequence you get 8-0=8.
What is the next number in this sequence 0,2,4,6,8......? Ans: The first number is 0. The second number is 2. The difference between those numbers is 2-0 = 2. The difference between the second and the third , the third and the fourth, the fourth and the fifty, the fifth and sixth is 2 only. So, the common difference is 2. That is 0+2=2, 2+2=4,4+2=6,6+2=8, then the next number in the series is 8+2 =10. The series continue like that only until infinity.
There are infinitely many different polynomials of degree 8 that will fit all the numbers of the above sequence. Each will generate a different number as the next one in the sequence.
4
16
64
It is 21 + 34 = 55
The sequence alternates between multiplying by 2 and then adding 2. Starting with 2, it goes to 4 (2×2), then to 8 (4×2), followed by 10 (8+2), and then to 20 (10×2). Following this pattern, the next operation would be adding 2 to 20, resulting in 22. Thus, the next number in the sequence is 22.